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At least 235 records · Page 13

Secure boot, trusted boot and remote attestation for ARM TrustZone-based IoT Nodes

With the extensive application of IoT techniques, IoT devices have become ubiquitous in daily lives. Meanwhile, attacks against IoT devices have emerged to compromise IoT devices by tampering with system pre-installed programs or injecting new malware. To mitigate these attacks, integrity enforcement of IoT systems has been proposed. The integrity of an IoT device system includes load-time integrity and runtime integrity. In this paper, we design an IoT system based on ARM TrustZone to enforce the system integrity. First, we establish the root of trust and propose a hybrid booting approach consisting of both secure boot and trusted boot to enforce the system load-time integrity. Second, we investigate a paging-based process integrity measurement method to measure the NW processes and conduct remote attestation based on the measurement results ensuring the NW runtime process integrity. We implement an IoT prototype system on a NXP i.MX6Q SABRE SD development board to assess its feasibility. Finally, real-world experiment results demonstrate that our prototype introduces negligible performance overhead to the original system.

97 MATHEMATICS AND COMPUTING↗

A flexible data acquisition system architecture for the Nab experiment

Here, the Nab experiment will measure the electron–neutrino correlation and Fierz interference term in free neutron beta decay to test the Standard Model and probe Beyond the Standard Model physics. Using National Instrument’s PXIe-5171 Reconfigurable Oscilloscope module, we have developed a data acquisition system that is not only capable of meeting Nab’s specifications, but flexible enough to be adapted in situ as the experimental environment dictates. The L1 and L2 trigger logic can be reconfigured to optimize the system for coincidence event detection at runtime through configuration files and LabVIEW controls. This system is capable of identifying L1 triggers at a rate of at least 1 MHz, while reading out a peak signal rate of approximately 2 GB/s. During the commissioning phase of the experiment, the system ran at a sustained readout rate of 400 MB/s of detector signal data originating from roughly 6 kHz L2 triggers, well within the peak performance of the system.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Locality-Aware Scheduling for Scalable Heterogeneous Environments

Heterogeneous computing promise boost performance of scientific applications by allowing massively parallel execution of computational tasks. However, manually managing extremely heterogeneous, multi-device systems is complicated and may result in sub-optimal performance. Specifically, data management is an extremely challenging problem on multi-device systems. In this work, we introduce two locality-aware schedulers for the Minos Computing Library (MCL), an asynchronous, task-based programming model and runtime for extremely heterogeneous systems. The first scheduler implements a pure locality-aware algorithm to maximize data reuse, though it might incur in ”hot-spots” that limit system utilization. The second scheduler mitigates this drawback by dynamically targeting between locality-awareness and system utilization based on the current workload and available computing devices. Our results show that locality-awareness greatly benefit applications that exhibit data reuse, providing up to 6.9x and 7.9x over the original MCL scheduler and equivalent OpenCL implementations, respectively. Moreover, our schedulers introduce negligible overhead compared with the original MCL scheduler and achieve similar performance for applications that don’t benefit from data locality.

Architecture, co-design, Task-based programming mo↗

Resiliency in numerical algorithm design for extreme scale simulations

Here this work is based on the seminar titled ‘Resiliency in Numerical Algorithm Design for Extreme Scale Simulations’ held March 1–6, 2020, at Schloss Dagstuhl, that was attended by all the authors. Advanced supercomputing is characterized by very high computation speeds at the cost of involving an enormous amount of resources and costs. A typical large-scale computation running for 48 h on a system consuming 20 MW, as predicted for exascale systems, would consume a million kWh, corresponding to about 100k Euro in energy cost for executing 10 23 floating-point operations. It is clearly unacceptable to lose the whole computation if any of the several million parallel processes fails during the execution. Moreover, if a single operation suffers from a bit-flip error, should the whole computation be declared invalid? What about the notion of reproducibility itself: should this core paradigm of science be revised and refined for results that are obtained by large-scale simulation? Naive versions of conventional resilience techniques will not scale to the exascale regime: with a main memory footprint of tens of Petabytes, synchronously writing checkpoint data all the way to background storage at frequent intervals will create intolerable overheads in runtime and energy consumption. Forecasts show that the mean time between failures could be lower than the time to recover from such a checkpoint, so that large calculations at scale might not make any progress if robust alternatives are not investigated. More advanced resilience techniques must be devised. The key may lie in exploiting both advanced system features as well as specific application knowledge. Research will face two essential questions: (1) what are the reliability requirements for a particular computation and (2) how do we best design the algorithms and software to meet these requirements? While the analysis of use cases can help understand the particular reliability requirements, the construction of remedies is currently wide open. One avenue would be to refine and improve on system- or application-level checkpointing and rollback strategies in the case an error is detected. Developers might use fault notification interfaces and flexible runtime systems to respond to node failures in an application-dependent fashion. Novel numerical algorithms or more stochastic computational approaches may be required to meet accuracy requirements in the face of undetectable soft errors. These ideas constituted an essential topic of the seminar. The goal of this Dagstuhl Seminar was to bring together a diverse group of scientists with expertise in exascale computing to discuss novel ways to make applications resilient against detected and undetected faults. In particular, participants explored the role that algorithms and applications play in the holistic approach needed to tackle this challenge. This article gathers a broad range of perspectives on the role of algorithms, applications and systems in achieving resilience for extreme scale simulations. The ultimate goal is to spark novel ideas and encourage the development of concrete solutions for achieving such resilience holistically.

79 ASTRONOMY AND ASTROPHYSICS↗

Scalable fault tolerance runtime technology for petascale computers (Final Project Report)

With the massive number of components comprising the forthcoming petascale computer systems, hardware failures will be routinely encountered during execution of large-scale applications. Due to the multidisciplinary, multiresolution, and multiscale nature of scientific problems that drive the demand for high end systems, applications place increasingly differing demands on the system resources: disk, network, memory, and CPU. In addition to MPI, future applications are expected to use advanced programming models such as those developed under the DARPA HPCS program as well as existing global address space programming models such as Global Arrays, UPC, and Co-Array Fortran. While there has been a considerable amount of work in fault tolerant MPI with a number of strategies and extensions for fault tolerance proposed, virtually none of advanced models proposed for emerging petascale systems is currently fault aware. To achieve fault tolerance, development of underlying runtime and OS technologies able to scale to petascale level is needed. This project has evaluated range of runtime techniques for fault tolerance for advanced programming models.

97 MATHEMATICS AND COMPUTING↗

A Scala DSL for RETE-Based Runtime Verification

Runtime verification (RV) consists in part of checking execution traces against formalized specifications. Several systems have emerged, most of which support specification notations based on state machines, regular expressions, temporal logic, or grammars. The field of Artificial Intelligence (AI) has for an even longer period of time studied rule-based production systems, which at a closer look appear to be relevant for RV, although seemingly focused on slightly different application domains, such as for example business processes and expert systems. The core algorithm in many of these systems is the Rete algorithm. We have implemented a Rete-based runtime verification system, named LogFire (originally intended for offline log analysis but also applicable to online analysis), as an internal DSL in the Scala programming language, using Scala's support for defining DSLs. This combination appears attractive from a practical point of view. Our contribution is in part conceptual in arguing that such rule-based frameworks originating from AI may be suited for RV.

matching problem↗

Three practical workflow schedulers for easy maximum parallelism

Runtime scheduling and workflow systems are an increasingly popular algorithmic component in HPC because they allow full system utilization with relaxed synchronization requirements. There are so many special-purpose tools for task scheduling, one might wonder why more are needed. Use cases seen on the Summit supercomputer needed better integration with MPI and greater flexibility in job launch configurations. Preparation, execution, and analysis of computational chemistry simulations at the scale of tens of thousands of processors revealed three distinct workflow patterns. A separate job scheduler was implemented for each one using extremely simple and robust designs: file-based, task-list based, and bulk-synchronous. Comparing to existing methods shows unique benefits of this work, including simplicity of design, suitability for HPC centers, short startup time, and well-understood per-task overhead. All three new tools have been shown to scale to full utilization of Summit, and have been made publicly available with tests and documentation. This work presents a complete characterization of the minimum effective task granularity for efficient scheduler usage scenarios. Here, these schedulers have the same bottlenecks, and hence similar task granularities as those reported for existing tools following comparable paradigms.

97 MATHEMATICS AND COMPUTING↗

Sandia Cloud Forensics and Incident Response Platform v 1.0

As systems and devices become virtualized and deployed in the cloud, the hypervisor becomes an increasingly appropriate place to collect performance data, system state, system landscape, function calls, transaction traces, and other characteristics. We developed a method by which an introspection application may be coupled with a hypervisor to “reach into” the VM with minimal intrusiveness to collect data critical to the reconstruction of events, files, and operations. Such a capability is required to take advantage of the hypervisor as an instrumentation platform and to integrate that data with more traditional collection mechanisms. The concept of a VM serviced by a lightweight hypervisor is a relatively new paradigm for forensic practitioners. Traditional forensic techniques, based on assumptions that the filesystem was directly interacting with the hardware through an abstraction, afforded the forensic practitioner the assumption that there was nothing controlling the application below the filesystem. This is not the case when using virtualized technologies. Hypervisors can covertly monitor, introspect and interact with the guest in a transparent fashion. The problems of storage and collection of actionable data are exhausting. The current challenge is most hypervisors do not expose a useful application programming interface (API) at a sufficient level to do transparent, fine-grained and customizable introspection. Scalable VM instrumentation and introspection at an in-depth level requires fast handling of events, as well as direct access to VM state. Furthermore, deep introspection benefits greatly from the ability to gather data from the hardware during the VM’s exit to the hypervisor. All of this requires identical access to the system as the hypervisor itself; improper use of this ability could easily cause system instability. It is for this reason we believe that the hypervisor developers have been hesitant to grant this much control through their APIs. However, our approach leverages other means to collect and monitor the guests in a targeted fashion. Virtual machine introspection (VMI) is a technique used to monitor the runtime state of a system-level virtual machine. The runtime state can be may include processor registers, memory, disk, network, and any other hardware-level events A review of research literature and current VMI technologies exposed several limitations and tradeoffs in VMI approaches, including: the use of in-guest agents; kernel to user space transitions (dramatically slowing down processing); VMI tool pre-configuration requirements; hypervisor version lock-in or source code patching; reliance on operating system symbols; limited processor features due to hypervisor (even if the hardware could do more). To address these constraints, a VMI tool was envisioned to provide the cloud forensic capabilities while having as few of these limitations as possible. The Kernel-based Virtual Machine Introspection (KVMi) tool was developed for hypervisors on Intel’s x86-64 architecture. To meet performance, scoping and use-case demands, the follow criteria were applied to KVMi to support live, forensic data collection: • Shall not require in-guest agents. • Shall work with any recent version of modern hypervisors. • Shall introspect upon any guest (VM) running modern versions of Windows, Linux and OS X. • Shall have the ability to find and track operating system artifacts • Shall not require operating system symbol files. • Shall be able to fully handle VM-exits, bypassing execution of the hypervisor if necessary, to facilitate new features the hypervisor may not support. • Shall be compilable/loadable on a running system with standard build tools.

Stout, WilliamM.S.↗

Intelligent Hardware-Enabled Sensor and Software Safety and Health Management for Autonomous UAS

Unmanned Aerial Systems (UAS) can only be deployed if they can effectively complete their mission and respond to failures and uncertain environmental conditions while maintaining safety with respect to other aircraft as well as humans and property on the ground. We propose to design a real-time, onboard system health management (SHM) capability to continuously monitor essential system components such as sensors, software, and hardware systems for detection and diagnosis of failures and violations of safety or performance rules during the ight of a UAS. Our approach to SHM is three-pronged, providing: (1) real-time monitoring of sensor and software signals; (2) signal analysis, preprocessing, and advanced on-the- y temporal and Bayesian probabilistic fault diagnosis; (3) an unobtrusive, lightweight, read-only, low-power hardware realization using Field Programmable Gate Arrays (FPGAs) in order to avoid overburdening limited computing resources or costly re-certi cation of ight software due to instrumentation. No currently available SHM capabilities (or combinations of currently existing SHM capabilities) come anywhere close to satisfying these three criteria yet NASA will require such intelligent, hardwareenabled sensor and software safety and health management for introducing autonomous UAS into the National Airspace System (NAS). We propose a novel approach of creating modular building blocks for combining responsive runtime monitoring of temporal logic system safety requirements with model-based diagnosis and Bayesian network-based probabilistic analysis. Our proposed research program includes both developing this novel approach and demonstrating its capabilities using the NASA Swift UAS as a demonstration platform.

Robotics↗

PRIMA-X Final Report

The PRIMA-X (Performance Retargeting of Instrumentation, Measurement, and Analysis Technologies for Exascale Computing) project is the successor of the DOE PRIMA (Performance Refactoring of Instrumentation, Measurement, and Analysis Technologies for Petascale Computing) project, which addressed the challenge of creating a core measurement infrastructure that would serve as a common platform for both integrating leading parallel performance systems (notably TAU and Scalasca) and developing next-generation scalable performance tools. The PRIMA-X project shifts the focus away from refactorization of robust performance tools towards a re-targeting of the parallel performance measurement and analysis architecture for extreme scales. The massive concurrency, asynchronous execution dynamics, hardware heterogeneity, and multi-objective prerequisites (performance, power, resilience) that identify exascale systems introduce fundamental constraints on the ability to carry forward existing performance methodologies. In particular, there must be a deemphasis of per-thread observation techniques to significantly reduce the otherwise unsustainable flood of redundant performance data. Instead, it will be necessary to assimilate multi-level resource observations into macroscopic performance views, from which resilient performance metrics can be attributed to the computational features of the application. This requires a scalable framework for node-level and system-wide monitoring and runtime analyses of dynamic performance information. Also, the interest in optimizing parallelism parameters with respect to performance and energy drives the integration of tool capabilities in the exascale environment further. Initially, PRIMA-X was a collaborative project between the University of Oregon (lead institution) and the German Research School for Simulation Sciences (GRS). Because Prof. Wolf, the PI at GRS, accepted a position as full professor at Technische Universität Darmstadt (TU Darmstadt) starting February 1st, 2015, the project ended at GRS on January 31st, 2015. This report reflects the work accomplished at GRS until then. The work of GRS is expected to be continued at TU Darmstadt. The first main accomplishment of GRS is the design of different thread-level aggregation techniques. We created a prototype capable of aggregating the thread-level information in performance profiles using these techniques. The next step will be the integration of the most promising techniques into the Score-P measurement system and their evaluation. The second main accomplishment is a substantial increase of Score-P’s scalability, achieved by improving the design of the system-tree representation in Score-P’s profile format. We developed a new representation and a distributed algorithm to create the scalable system tree representation. Finally, we developed a lightweight approach to MPI wait-state profiling. Former algorithms either needed piggy-backing, which can cause significant runtime overhead, or tracing, which comes with its own set of scaling challenges. Our approach works with local data only and, thus, is scalable and has very little overhead.

97 MATHEMATICS AND COMPUTING↗

SPARTAN: A High-Fidelity Simulation for Automated Rendezvous and Docking Applications

bd Systems (a subsidiary of SAIC) has developed the Simulation Package for Autonomous Rendezvous Test and ANalysis (SPARTAN), a high-fidelity on-orbit simulation featuring multiple six-degree-of-freedom (6DOF) vehicles. SPARTAN has been developed in a modular fashion in Matlab/Simulink to test next-generation automated rendezvous and docking guidance, navigation,and control algorithms for NASA's new Vision for Space Exploration. SPARTAN includes autonomous state-based mission manager algorithms responsible for sequencing the vehicle through various flight phases based on on-board sensor inputs and closed-loop guidance algorithms, including Lambert transfers, Clohessy-Wiltshire maneuvers, and glideslope approaches The guidance commands are implemented using an integrated translation and attitude control system to provide 6DOF control of each vehicle in the simulation. SPARTAN also includes high-fidelity representations of a variety of absolute and relative navigation sensors that maybe used for NASA missions, including radio frequency, lidar, and video-based rendezvous sensors. Proprietary navigation sensor fusion algorithms have been developed that allow the integration of these sensor measurements through an extended Kalman filter framework to create a single optimal estimate of the relative state of the vehicles. SPARTAN provides capability for Monte Carlo dispersion analysis, allowing for rigorous evaluation of the performance of the complete proposed AR&D system, including software, sensors, and mechanisms. SPARTAN also supports hardware-in-the-loop testing through conversion of the algorithms to C code using Real-Time Workshop in order to be hosted in a mission computer engineering development unit running an embedded real-time operating system. SPARTAN also contains both runtime TCP/IP socket interface and post-processing compatibility with bdStudio, a visualization tool developed by bd Systems, allowing for intuitive evaluation of simulation results. A description of the SPARTAN architecture and capabilities is provided, along with details on the models and algorithms utilized and results from representative missions.

Turbe, Michael A.↗

Q-IRIS: The Evolution of the IRIS Task-Based Runtime to Enable Classical-Quantum Workflows

Extreme heterogeneity in emerging HPC systems are starting to include quantum accelerators, motivating runtimes that can coordinate between classical and quantum workloads. We present a proof-of-concept hybrid execution framework integrating the IRIS asynchronous task-based runtime with the XACC quantum programming framework via the Quantum Intermediate Representation Execution Engine (QIR-EE). IRIS orchestrates multiple programs written in the quantum intermediate representation (QIR) across heterogeneous backends (including multiple quantum simulators), enabling concurrent execution of classical and quantum tasks. Although not a performance study, we report measurable outcomes through the successful asynchronous scheduling and execution of multiple quantum workloads. To illustrate practical runtime implications, we decompose a four-qubit circuit into smaller subcircuits through a process known as quantum circuit cutting, reducing per-task quantum simulation load and demonstrating how task granularity can improve simulator throughput and reduce queueing behavior -- effects directly relevant to early quantum hardware environments. We conclude by outlining key challenges for scaling hybrid runtimes, including coordinated scheduling, classical-quantum interaction management, and support for diverse backend resources in heterogeneous systems.

Miniskar, Narasinga Rao [ORNL] (ORCID:000000018259↗

Design and analysis of optimal pre-cooling in residential buildings

Existing pre-cooling strategies provide a means of shifting or reducing the peak demand and/or energy cost in residential buildings. However, majority of them are rule-based and therefore may not be optimal in terms of cost saving, leaving room for improvement. In this paper, an integer linear programming problem that accounts for the thermal properties of a specific home, HVAC system capacity, utility rate structure, and weather conditions and makes use of a home thermal model is formulated. This problem determines the HVAC on/off control signal that minimizes the 24-h energy cost while maintaining thermal comfort and calculates the corresponding optimal indoor air temperature. The model is constructed using home thermal properties identified via data training in real-time. Through simulation, the energy performance of the proposed optimal pre-cooling strategy is investigated and compared with three rule-based operation strategies from the literature. It is found that the optimal strategy requires the least energy consumption without sacrificing thermal comfort. The superb energy performance of the optimal strategy is attributed to a longer runtime of the HVAC system in cool outdoor air conditions and to the elimination of deadband in HVAC operation, which is required by the rule-based strategies, to allow the indoor air temperature to stay near the thermal comfort upper bound as much as possible. In terms of energy cost, the rule-based operation strategies require 3.52, 1.90, and 2.79, respectively, while the optimal strategy only requires 1.52. These figures represent a saving of 56.82%, 20.00%, and 45.52%, respectively. The results suggest that the optimal strategy is indeed significantly more effective than the existing rule-based operation strategies.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

A Scientific Data Provenance Harvester for Distributed Applications

Data provenance provides a way for scientists to observe how experimental data originates, conveys process history, and explains influential factors such as experimental rationale and associated environmental factors from system metrics measured at runtime. The US Department of Energy Office of Science Integrated end-to-end Performance Prediction and Diagnosis for Extreme Scientific Workflows (IPPD) project has developed a provenance harvester that is capable of collecting observations from file based evidence typically produced by distributed applications. To achieve this, file based evidence is extracted and transformed into an intermediate data format inspired in part by W3C CSV on the Web recommendations, called the Harvester Provenance Application Interface (HAPI) syntax. This syntax provides a general means to pre-stage provenance into messages that are both human readable and capable of being written to a provenance store, Provenance Environment (ProvEn). HAPI is being applied to harvest provenance from climate ensemble runs for Accelerated Climate Modeling for Energy (ACME) project funded under the U.S. Department of Energy’s Office of Biological and Environmental Research (BER) Earth System Modeling (ESM) program. ACME informally provides provenance in a native form through configuration files, directory structures, and log files that contain success/failure indicators, code traces, and performance measurements. Because of its generic format, HAPI is also being applied to harvest tabular job management provenance from Belle II DIRAC scheduler relational database tables as well as other scientific applications that log provenance related information.

Stephan, Eric G.↗

PRIMA-X - Performance Retargeting of Instrumentation, Measurement, and Analysis Technologies for Exascale Computing

The PRIMA-X (Performance Retargeting of Instrumentation, Measurement, and Analysis Technologies for Exascale Computing) project is the successor of the DOE PRIMA (Performance Refactoring of Instrumentation, Measurement, and Analysis Technologies for Petascale Computing) project, which addressed the challenge of creating a core measurement infrastructure that would serve as a common platform for both integrating leading parallel performance systems (notably TAU and Scalasca) and developing next-generation scalable performance tools. The PRIMA-X project shifts the focus away from refactorization of robust performance tools towards a re-targeting of the parallel performance measurement and analysis architecture for extreme scales. The massive concurrency, asynchronous execution dynamics, hardware heterogeneity, and multi-objective prerequisites (performance, power, resilience) that identify exascale systems introduce fundamental constraints on the ability to carry forward existing performance methodologies. In particular, there must be a deemphasis of per-thread observation techniques to significantly reduce the otherwise unsustainable flood of redundant performance data. Instead, it will be necessary to assimilate multi-level resource observations into macroscopic performance views, from which resilient performance metrics can be attributed to the computational features of the application. This requires a scalable framework for node-level and system-wide monitoring and runtime analyses of dynamic performance information. Also, the interest in optimizing parallelism parameters with respect to performance and energy drives the integration of tool capabilities in the exascale environment further. Initially, PRIMA-X was a collaborative project between the University of Oregon (lead institution) and the German Research School for Simulation Sciences (GRS). Because Prof. Wolf, the PI at GRS, accepted a position as full professor at Technische Universitaet Darmstadt (TU Darmstadt) starting February 1st, 2015, the work of GRS was continued at TU Darmstadt. This report covers the work at TU Darmstadt after the transition. The first main accomplishment of TU Darmstadt is the development of different techniques to aggregate performance data on the level of threads. TU Darmstadt evaluated different schemes designed at GRS during the first phase of this project and integrated them into Score-P, a widely used performance measurement framework for HPC applications. The second main accomplishment is a substantial increase of Score-P’s scalability, achieved by improving its internal representation of the underlying system. Third, we extended our performance-modeling tool Extra-P to automatically create models with more than one input parameter (e.g., process count and input size), which was previously impossible. These models allow the performance behavior of an application to be extrapolated to larger machines. Specific applications of the new multi-parameter capability realized in this project include modeling the isoefficiency function of task-based applications and a novel co-design methodology. Further extensions of Extra-P comprise online modeling functionality, automatic refinement of the model search space, and segmented performance modeling. Further contributions include new locality metrics for both shared- and distributed-memory applications, a new way of measuring the impact of inter-application inference on the execution time of an application, and finally an automatic method that selects appropriate OpenMP constructs for the parallelization of sequential code and classifies the affected variables based on their sharing semantics.

97 MATHEMATICS AND COMPUTING↗

pnnl/mcl-runtime

The Minos Computing Library (MCL) is a task-based programming language and runtime for extremely heterogeneous systems. MCL facilitates writing program for heterogeneous devices and porting applications across different systems and devices. MCL supports asynchronous execution of computing tasks on all available heterogeneous devices, including GPUs, FGPAs, fixed-point accelerators, and AI accelerators. MCL provides a high-level programming interface and automatically and autonomously performs resource management, load balancing, and locality-aware scheduling.

Central, PNNL Developer↗

Numerical eigen-spectrum slicing, accurate orthogonal eigen-basis, and mixed-precision eigenvalue refinement using OpenMP data-dependent tasks and accelerator offload

Performing a variety of numerical computations efficiently and, at the same time, in a portable fashion requires both an overarching design followed by a number of implementation strategies. All of these are exemplified below as we present transitioning the PLASMA numerical library from relying on dependence-driven large tasks to achieving utilization of fine grain tasking and offload to hardware accelerators while keeping its core dependence sets: OpenMP source code pragmas and runtime for most system-level functionality and basic low-level numerical kernels provided directly by hardware vendors or open source projects with vendor contributions. We also present new algorithmic methods and their efficient parallel implementations including fine grained tasking for eigen-spectrum slicing and offload for mixed-precision eigenvalue refinement. We provide performance, scaling, and numerical results showing sizable gains over the available solutions from either the open source and vendor-provided packages.

Luszczek, Piotr↗